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Exact effective interactions and 1/4-BPS dyons in heterotic CHL orbifolds
by Guillaume Bossard, Charles Cosnier-Horeau, Boris Pioline
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Submission summary
Authors (as registered SciPost users): | Boris Pioline |
Submission information | |
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Preprint Link: | https://arxiv.org/abs/1806.03330v2 (pdf) |
Date accepted: | Aug. 26, 2019 |
Date submitted: | June 10, 2019, 2 a.m. |
Submitted by: | Pioline, Boris |
Submitted to: | SciPost Physics |
Ontological classification | |
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Academic field: | Physics |
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Approach: | Theoretical |
Abstract
Motivated by precision counting of BPS black holes, we analyze six-derivative couplings in the low energy effective action of three-dimensional string vacua with 16 supercharges. Based on perturbative computations up to two-loop, supersymmetry and duality arguments, we conjecture that the exact coefficient of the ∇2(∇ϕ)4 effective interaction is given by a genus-two modular integral of a Siegel theta series for the non-perturbative Narain lattice times a specific meromorphic Siegel modular form. The latter is familiar from the Dijkgraaf-Verlinde-Verlinde (DVV) conjecture on exact degeneracies of 1/4-BPS dyons. We show that this Ansatz reproduces the known perturbative corrections at weak heterotic coupling, including tree-level, one- and two-loop corrections, plus non-perturbative effects of order e−1/g23. We also examine the weak coupling expansions in type I and type II string duals and find agreement with known perturbative results, as well as new predictions for higher genus perturbative contributions. In the limit where a circle in the internal torus decompactifies, our Ansatz predicts the exact ∇2F4 effective interaction in four-dimensional CHL string vacua, along with infinite series of exponentially suppressed corrections of order e−R from Euclideanized BPS black holes winding around the circle, and further suppressed corrections of order e−R2 from Taub-NUT instantons. We show that instanton corrections from 1/4-BPS black holes are precisely weighted by the BPS index predicted from the DVV formula, including the detailed moduli dependence. We also extract two-instanton corrections from pairs of 1/2-BPS black holes, demonstrating consistency with supersymmetry and wall-crossing, and estimate the size of instanton-anti-instanton contributions.
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Published as SciPost Phys. 7, 028 (2019)